Results 31 to 40 of about 7,475 (192)

Fractional Calculus for Non-Discrete Signed Measures

Mathematics
In this paper, we suggest a first-ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann–Stieltjes integral with a
Vassili N. Kolokoltsov, Elina L. Shishkina   +1 more
doaj   +1 more source

Riemann-Stieltjes integration in Riesz spaces [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 1996
After introducing an integral for Riesz-space valued integral functions, this concept is used to represent the variation of a continuous function, to define integrals along a curve and Riemann-Stieltjes integrals, and to deduce from them, as particular
D. CANDELORO
doaj  

Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition

Advances in Difference Equations, 2018
In this article, the following boundary value problem of fractional differential equation with Riemann–Stieltjes integral boundary condition {D0+αu(t)+λf(t,u(t),u(t))=0 ...
Qilin Song, Zhanbing Bai
doaj   +1 more source

Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions [PDF]

Opuscula Mathematica, 2018
We study second-order linear Sturm-Liouville problems involving general homogeneous linear Riemann-Stieltjes integral boundary conditions. Conditions are obtained for the existence of a sequence of positive eigenvalues with consecutive zero counts of the
Qingkai Kong, Thomas E. St. George
doaj   +1 more source

Fractional L\'{e}vy-driven Ornstein--Uhlenbeck processes and stochastic differential equations

, 2011
Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\'{e}vy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-
Fink, Holger, Klüppelberg, Claudia
core   +1 more source

Moments of the Riemann zeta function at its local extrema

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non‐trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of the Riemann zeta function evaluated at its local extrema along the critical line to leading order.
Andrew Pearce‐Crump
wiley   +1 more source

Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann-Stieltjes Integral Conditions

Abstract and Applied Analysis, 2012
The existence of at least one positive solution is established for a class of semipositone fractional differential equations with Riemann-Stieltjes integral boundary condition. The technical approach is mainly based on the fixed-point theory in a cone.
Wei Wang, Li Huang
doaj   +1 more source

Inequalities and majorisations for the Riemann-Stieltjes integral on time scales

, 2010
We prove dynamic inequalities of majorisation type for functions on time scales. The results are obtained using the notion of Riemann-Stieltjes delta integral and give a generalization of [App. Math. Let. 22 (2009), no.
Mozyrska, Dorota, Pawluszewicz, Ewa, Torres, Delfim F. M.   +2 more
core   +1 more source

Pathwise convergence of the Euler scheme for rough and stochastic differential equations

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract The convergence of the first‐order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by càdlàg paths satisfying a suitable criterion, namely the so‐called Property (RIE), along time discretizations with vanishing mesh size. This property is then verified for
Andrew L. Allan, Anna P. Kwossek, Chong Liu, David J. Prömel   +3 more
wiley   +1 more source

Rough PDEs for Local Stochastic Volatility Models

Mathematical Finance, Volume 35, Issue 3, Page 661-681, July 2025.
ABSTRACT In this work, we introduce a novel pricing methodology in general, possibly non‐Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time‐inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely
Peter Bank, Christian Bayer, Peter K. Friz, Luca Pelizzari   +3 more
wiley   +1 more source