相关论文: Exact Pathwise and Mean--Square Asymptotic Behavio…
This paper considers the growth rates of positive solutions of scalar nonlinear functional and Volterra differential equations. The equations are assumed to be autonomous (or asymptotically so), and the nonlinear dependence grows less…
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state,…
This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…
We investigate memory dependent asymptotic growth in scalar Volterra equations with sublinear nonlinearity. To obtain precise results we utilise the powerful theory of regular variation extensively. By computing the growth rate in terms of…
True Volterra equations are inherently non stationary and therefore do not admit $\textit{genuine stationary regimes}$ over finite horizons. This motivates the study of the finite-time behavior of the solutions to scaled inhomogeneous…
This paper studies the large fluctuations of solutions of finite--dimensional affine stochastic neutral functional differential equations with finite memory, as well as related nonlinear equations. We find conditions under which the exact…
We investigate the properties of the solutions of scaled Volterra equations (i.e. with an affine mean-reverting drift) in terms of stationarity at both a finite horizon and on the long run. In particular we prove that such an equation never…
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…
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contributions of the average and instantaneous terms are…
We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
This paper studies the asymptotic growth and decay properties of solutions of the stochastic pantograph equation with multiplicative noise. We give sufficient conditions on the parameters for solutions to grow at a polynomial rate in $p$-th…
In this paper, we determine rates of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of a nonlinear…
We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper…
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
In this paper, we study the time-space fractional differential equation of the Volterra type: \begin{align*} {D}^\alpha_{0 \vert t} (u) +(-\Delta_N)^{\sigma}u &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds, \end{align*} where $a,b>0$…
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main result provide sufficient…
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition…
We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.