Related papers: Affine Volterra processes

We study the linear convergence of variants of the Frank-Wolfe algorithms for some classes of strongly convex problems, using only affine-invariant quantities. As in Guelat & Marcotte (1986), we show the linear convergence of the standard…

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra…

A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties of Volterra processes and reviewing existing numerical…

We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special…

We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…

We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…

In this paper we give a survey of results on various analytical aspects of time fractional diffusion equations. We describe the approach via abstract Volterra equations and collect results on strong solutions in the $L_p$ sense. We further…

Multivariate process satisfying affine stochastic recurrence equation with generic diagonal matrices is considered. We prove that the stationary solution is regularly varying. The results are applicable to diagonal autoregressive models.

In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…

To describe stochastic quantum processes I propose an integral equation of Volterra type which is not generally transformable to any differential one. The process is a composition of ordinary quantum evolution which admits presence of a…

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also…

A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…

We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein-Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic…

This review summarizes all known results (up to this date) about methods of integration of the classical Lotka-Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability…

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using…

This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…

We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…

In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $\alpha$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential…

By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…

This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…