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Showing 1 to 20 of 20 for “"Brownian motions"”.
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Brownian motions on a Riemannian manifold
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1961.
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Potential theory of subordinate Brownian motions and their perturbations
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-04-09T16:14:28Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Hyunchul_Park.pdf: 539321 bytes, checksum: bcfd0a5064cd6d8ec336a32baba3522b (MD5)
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Intrinsic Ultracontractivity and Other Properties of Mixed Barrier Brownian Motions
… parts. First, we study an asymptotic behavior of Brownian motions with Dirichlet boundary condition on an unbounded domain D above the graph of a bounded Lipschitz function. We discover that the large time behavior of the Dirichlet heat kernel pD = pD(t , x, y), for x, y ∈ D is …
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An Exponential Formula for Random Variables Generated by Multiple Brownian Motions
… for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or fractional conditional expectation in the case of fractional Brownian motion)and …
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Brownian particles interacting with a Newtonian Barrier: Skorohod maps and their use in solving a PDE with free boundary, strong approximation, and hydrodynamic limits.
… laws of motion, and the other particle being Brownian. In the first chapter we construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. The resulting PDE is …
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Convex hulls of planar random walks
… defined in terms of convex hulls of certain Brownian motions. We give bounds that confirm that the limiting variances in our results are non-zero.
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Complex dynamics of a microwave time-delayed feedback loop
… can have properties of a regular or fractional Brownian motion. By unidirectional coupling two systems in the baseband, envelope synchronization between two deterministic Brownian motions can be achieved.
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On intrinsic ultracontractivity of perturbed Levy processes and applications of Levy processes in actuarial mathematics
… of the Laplacian (corresponding to Brownian motions) and the fractional Laplacian (corresponding to symmetric $\alpha$-stable processes) perturbed by a class of nonlocal operators. Conditions on the nonlocal perturbations are given in order to guarantee that the perturbed operators …
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Mean-variance hedging in an illiquid market
… where the two assets are driven by correlated Brownian motions and the derivative is a call option on the illiquid asset. We use this example to compare the terminal hedging profit and loss of the optimal strategy to a corresponding strategy that does not use the static hedge in the illiquid …
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Modelling of asset allocation in banking using the mean-variance approach
… the different assets are modelled as geometric Brownian motions, and our optimization problem is of the mean- variance type. We assume the Basel II regulations on banking supervision. In this contribution, the bank funds are invested into loans and treasuries with the main objective being to …
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Sieve bootstrap based prediction intervals and unit root tests for time series
… can be expressed as functional of the standard Brownian motions. Currently, the asymptotic results are available only for non-seasonal time series"--Abstract, page v.</p>
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Effects of particle shape and flexibility on suspension dynamics
… the particles under shear flow in the absence of Brownian motions to the steady state non-linear elasticity. We discuss briefly how our approach may be extended to concentrated suspensions and the transition to liquid crystalline states for these particles.
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Mathematical model of performance measurement of defined contribution pension funds
… uncertainty in the financial market is driven by Brownian motions. Numerical simulations were performed to compare the different models.
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Stochastic modelling of nutrient and predator-prey populations
… Then we study how the correlations between the Brownian motions affect the long-time properties of the system. The parametric conditions for the system to have a stationary distribution are deduced. Numerical simulations are carried out to substantiate the analytical results.
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On the exact simulation of (skew) Brownian diffusions with discontinuous drift
… exact simulation of two classes of real-valued Brownian diffusions: multi-skew Brownian motions with constant drift and Brownian diffusions whose drift admits a finite number of jumps. The skew Brownian motion was introduced in the sixties by Itô and McKean, who constructed it from the reflected …
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Deterministic and Stochastic Approaches to Relaxation to Equilibrium for Particle Systems
… equation. In the second we couple the driving Brownian motions of two solutions with different initial data, in a well chosen way, to show convergence. Next we look at a classical tool to show convergence to equilibrium for Markov processes, Harris's theorem. We use this to show quantitative …
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Asymptotics, exact results, and analogies in p-adic random matrix theory
… fluctuations converge dynamically to independent Brownian motions. (6) We classify left GLₙ(Qₚ)-invariant stochastic processes on the (discrete) homogeneous space GLₙ(Qₚ)/GLₙ(Zₚ) with independent increments. We consider the one with smallest jumps, a p-adic analogue of multiplicative Brownian …
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Analytical Solutions of the SABR Stochastic Volatility Model
… finally the correlation between the two driving Brownian motions. We look at the problem from a PDE perspective where the joint transition density follows a linear second order equation of parabolic type in non-divergence form with coordinate-dependent coefficients. Particularly, we construct an …
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Lagrangian dynamics of turbulence: Applications with 3D particle tracking velocimetry
… coherent $t^2$-Batchelor scaling and then $t^1$-Brownian motions. Kolmogorov microscales during the fully mixed phase were computed with three distinct approaches, including Heisenberg-Yaglom relation, the fluctuating rate of the strain tensor in the Eulerian frame, and the Batchelor scaling in …
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Stochastic Models in Phylogenetic Comparative Methods: Analytical Properties and Parameter Estimation
… developed conditioned branching processes, with Brownian and Ornstein-Uhlenbeck evolution on top, expected species similarities are derived, together with phylogenetic confidence intervals for the optimal trait value. Finally, inspired by these developments, the phylogenetic framework is …