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In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as introduced in [2]. By using this fact, we are able to embed…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process…
The response to a setpoint change in PID controlled feedback systems plays an important role for the tuning methods. This response may be easily evaluated in linear systems without delay by solving the related ordinary differential…
In this paper we present a new method for deriving It\^{o} stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME,…
We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carath\'eodory-type drift coefficients. Moreover, we also assume that both drift $f=f(t,x,z)$ and diffusion…
A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be convergent in mean-square sense under conditions…
A fractional advection-dispersion equation (fADE) has been advocated for heavy-tailed flows where the usual Brownian diffusion models fail. A stochastic differential equation (SDE) driven by a stable L\'{e}vy process gives a forward…
It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an…
We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that…
We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated…
In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…