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Showing 1 to 20 of 97 for “"Stochastic Differential Equations"”.
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Algebraic structures in stochastic differential equations
We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize …
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Stability Theorems for Stochastic Differential Equations
… with the stability property for a sequence of stochastic differential equations when the limit process is a generalized diffusion type equation. The main result is an extention of a theorem of K. Yamada.
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Backward stochastic differential equations with jumps are stable
A backward stochastic differential equation is a stochastic differential equation whose terminal value is known, in contrast to a (forward) stochastic differential equation whose initial value is known, and whose solution has to be adapted to a given filtration. The main aim of this thesis is to …
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Linear and nonlinear stochastic differential equations with applications
… developed in the area of nonlinear and linear stochastic differential equations and applications are considered to a variety of physical problems. First, a method is introduced for deriving first- and second-order moment equations for a general class of stochastic nonlinear equations by …
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Statistical Inference for Stochastic Differential Equations using Splitting Schemes
… observed nonlinear first- and second-order stochastic differential equations (SDEs), focusing on splitting schemes and their applications. <br /> Initially, new numerical properties of splitting schemes, specifically the Lie-Trotter and Strang schemes, are established, enabling more accurate …
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Complexity Analysis of Quantizations of Multidimensional Stochastic Differential Equations
… located in the field of quantizations of certain stochastic processes, namely a solution X of a multidimensional stochastic differential equation (SDE). The quantization problem for X consists in approximating X by a a random element which takes only finitely many values. Our main interest lies in …
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Spectral Solution Method for Distributed Delay Stochastic Differential Equations
Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of …
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The new stochastic integral and anticipating stochastic differential equations
In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the Itô isometry that accounts for both adapted and instantly independent …
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Quasi-potential analysis of multi-variate stochastic differential equations
… first principles, I derive the deterministic equations describing these systems. Then, I derive the sources of noise and stochasticity based on basic probability theory. Stochastic differential equations are derived for these systems. Finally, I introduce and implement vector field …
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Construction and analysis of numerical methods for stochastic differential equations
Contains fulltext : 307491.pdf (Publisher’s version ) (Open Access)
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Local polynomial chaos expansion method for high dimensional stochastic differential equations
… in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the efficiency brought by PC expansion compared to sampling-based Monte Carlo experiments, but still suffered from relatively high simulation cost when …
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Using Data Augmentation and Stochastic Differential Equations in Spatio Temporal Modeling
… treating the inference when modeling using stochastic differential equations (SDE) that are partially observed has been growing in recent years. Many attempts have been made to tackle this problem, from very different perspectives. The goal of this thesis is not a comparison of the different …
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Enlargement of Filtration, Backward Stochastic Differential Equations and Optimal Stopping Problems
… of the enlargement of filtration to backward stochastic differential equations (BSDEs) and optimal stopping problems. In particular, the thesis develops the theory of the progressive enlargement of filtration with multiple random times and their associated marks. Several extensions of the …
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Numerical approximation and parametric statistical inference of stochastic differential equations, with applications to finance
Stochastic differential equations (SDEs) have become an indispensable tool for modelling the dynamics of key state variables in mathematical finance such as instantaneous short rates of interest, share prices, and volatility processes. The appropriate application of SDEs requires reliable methods …
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Adaptive mesh construction for the numerical solution of stochastic differential equations with Markovian switching
… approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are subject to random state changes according to a Markov chain with finite state …
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Combinatorics of a family of stochastic differential equations with an eye towards topological temperature
… a classification of a class of scale-separated stochastic differential equations is achieved using combinatorics and formal language theory. This is extended to a topological notion of temperature and qualitative results regarding the relatedness of scale separated stochastic dynamical systems …
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Point symmetry methods for Itô Stochastic Differential Equations (SDE) with a finite jump process
… the Lie point symmetry theory of deterministic differential equations to the class of jump-diffusion stochastic differential equations, i.e., a stochastic process driven by both Wiener and Poisson processes. The Poisson process generates the jumps whereas the Brownian motion path is continuous. …
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On optimal error rates for strong approximation of stochastic differential equations with irregular drift coefficients
… dissertation we study strong approximation of stochastic differential equations (SDEs) with irregular drift coefficients at the final time point or globally in time by methods that use only finitely many evaluations of the driving Brownian motion. We show the optimality of well-known methods, …
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