Deterministic vs. Stochastic Differential Equations
Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations
... Due to the wide range of scales in these solutions, it is extremely challenging to resolve the small scales of the solutions by direct numerical simulation. Tremendous computational resources are required to solve for ...
118
Stochastic vs. deterministic models for systems with delays
... Corresponding Deterministic System For The Stochastic Model With A Random Delay In [19], Schlicht and Winkler showed that if all the tran- sition rates are linear, then the mean solution of the ...
6
Stochastic Taylor Methods for Stochastic Delay Differential Equations
... most deterministic and stochastic numerical ...the stochastic Taylor expansion in equation (20), it enables us to construct a numerical method of high ...
11
Quasilinear Stochastic Partial Differential Equations
... Quasilinear stochastic PDE’s occur in applications such as the stochastic Navier-Stokes equation for which there is a complete answer to existence and uniqueness of ...The stochastic term in each of ...
88
Stochastic differential equations and integrating factor
... and deterministic differential equations are fundamentals for the modeling in science, en- gineering and mathematical ...accurate differential equation models and solve more demanding ...be ...
6
The Osgood condition for stochastic partial differential equations
... We end this introduction with some remarks concerning local existence of solutions when the equations are defined on the whole space. D. Khoshnevisan pointed to us that since for any fixed t > 0, the last term of ...
19
Stochastic differential equations in a scale of Hilbert spaces
... The aim of the present work is to extend Ovsyannikov’s method to the case of stochastic differential equations. We require the drift f to be a map from X α to X β for any α < β and satisfy a ...
21
Recursive Bayesian inference on stochastic differential equations
... be deterministic functions of the state, but would have certain distribution of possible ...truly stochastic, but the stochasticity is only used for representing the model ...
248
On the Effects of Different Interpretations of Stochastic Differential Equations
... the stochastic differential equ- ations is addressed from an applicative point of ...a stochastic integral with respect to a Brownian motion, there are infinite interpretations, and hence infinite ...
16
Numerical methods for simulation of stochastic differential equations
... Keywords: stochastic differential equations; Monte Carlo methods; Euler-Maruyama method; Milstein method 1 Introduction Until recently, many of the models ignored stochastic effects because of difficulty ...
10
Improved bridge constructs for stochastic differential equations
... a deterministic way, and another as a residual stochastic ...ordinary differential equation (ODE) system based on the drift, from the target ...
16
Discretisations of rough stochastic partial differential equations
... Stochastic PDEs are used to describe many physical, biological and econom- ical systems which, in contrast to deterministic systems, are subject to a random “noise”, see e.g. [BS95, GLP99, HL09]. This ...
166
Existence and Uniqueness of Solutions for Stochastic Differential Equations
... pp. stochastic dierential equations, stochastic analysis, stochastic integration Stochastic dierential equations arise typically in situations where, for instance, the time ...
65
Backward stochastic differential equations with Young drift
... in stochastic filtering, (Dan and et al 2013) gives a formal meaning to the mixed SDE by using a flow decompo- sition which separates the stochastic integration from the deterministic rough path ...
17
Path Integral Methods for Stochastic Differential Equations
... This loop correction arises because of two types of vertices. There are vertices that we call “branching” (as in Fig. 4), which have more exiting edges then entering edges. The opposite case occurs for those vertices ...
35
Strong approximation for Itô stochastic differential equations
... by deterministic ordinary differential equations ...few equations, the study of numerical methods have become more important and these must be designed to be implemented with a certain order ...
13
Stability of the Stochastic Differential Equations
... of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its ...concrete stochastic dynamical systems, conditions of existence the ...
5
Switching Game of Backward Stochastic Differential Equations and Associated System of Obliquely Reflected Backward Stochastic Differential Equations
... This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a ...
22
Stochastic control representations for penalized backward stochastic differential equations
... Penalized BSDE is nothing but a random time discretization of the optimal stopping representation for the corresponding reflected BSDE, where the time is discretized by Poisson arrival times. Acknowledgments. The author ...
25
Stochastic Runge-Kutta method for stochastic delay differential equations
... specifically stochastic Runge–Kutta with time delay, we propose to derive SRK for SDDE in this research as well as to approximate the strong solution of SDDE via this ...of differential equations, ...
30