If BB and f(B)f(B) are Brownian motions, then ff is affine

It is shown that if the processes $B$ and $f(B)$ are both Brownian motions (without a random time change) then $f$ must be an affine function. As a by-product of the proof, it is shown that the only functions which are solutions to both the Laplace equation and the eikonal equation are affine.Comment: 4 page

Inequalities for the Gaussian measure of convex sets

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions

Inequalities for the Gaussian measure of convex sets

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions

On certain classes of p-Valent functions by using complex-order and differential subordination.

The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z(Ip)r, ?(f(z))(j+1)/(p - j)(?p(r, ?)f(z))(j) < (a + (aB + (A- B)ß)z)/a(1 + Bz), where ?p(r, ?) is an operator defined by Salagean and ßis a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting properties

Uniform bounds for Black--Scholes implied volatility

In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulas for implied volatility at extreme strikes and/or maturities

Flexomagnetoelectric effect in bismuth ferrite

There is a profound analogy between inhomogeneous magnetoelectric effect in multiferroics and flexoelectric effect in liquid crystals. This similarity gives rise to the flexomagnetoelectric polarization induced by spin modulation. The theoretical estimations of flexomagnetoelectric polarization agree with the value of jumps of polarization in magnetoelectric dependences (~20muC/m^2) observed at spin cycloid suppression at critical magnetic field 200kOe.Comment: 6 pages,2 figure