The discrete Lotka–Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natura...

Discrete Lotka-Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with the non-Archimedean valuations and the space given by taking ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations in the previous report (solv-int/9906011). In this article, using the natural projection from p-adic intege...

Non-linear generalised minimum variance control state space design for a second-order Volterra series model Mohsen Maboodia,∗, Eduardo F. Camachob and Ali Khaki-Sedigha Industrial Control Center of Excellence, Department of Systems and Control Engineering, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran; Department of Systems Engineering and Automation, Uni...

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as space-dependent, so-called Fokker-Planck diffusion. The invader’s diffusion is taken as neutral Fickian. Furthermore, it is studied how multiplicative environmental noise ...

In the following paper, we provide a stochastic analogue to work of Shea and Wainger by showing that when the measure and state-independent diffusion coefficient of a linear Itô–Volterra equation are in appropriate Lp– weighted spaces, the solution lies in a weighted Lp–space in both an almost sure and moment sense.

In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations.

We establish pathwise continuity properties of solutions to a stochastic Volterra equation with an additive noise term given by a local martingale. The deterministic part is governed by an operator with an H∞-calculus and a scalar kernel. The proof relies on the dilation theorem for positive definite operator families on a Hilbert space.

The ”freezing” method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type x(t)− ∫ t 0 K(t, t− s)x(s)ds = f(t) (t ≥ 0), where K(t, s) is an operator valued function ”slowly” varying in the first argument. Besides, sharp explicit stability conditions are derived. Subject Classification: 45M10, 45N05

This report introduces the ideas behind particle filters, looking at the Kalman filter and the SIS and SIR filters to learn about the latent state of state space models. It then introduces particle MCMC as a way of learning about the parameters behind these models. Finally, the SIR filter and particle MCMC algorithms are applied to reaction networks, in particular the Lotka Volterra model.

In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval [0, 1]. 200 Mathematics Subject Classification: 26A33, 45J05, 39B05, 34A60, 34G20, 34K05.