I am interested in the range of velocity changes of missiles. Planes have a minimum speed set equal to the landing speed, helicopters also have a set speed - this is zero, but what about missiles? Anti-ship and anti-radar missiles have a well-defined trajectory, however, their maximum and average speeds are determined in the documentation. Which traffic sections do they correspond to? And is it possible to somehow estimate the minimum speed of missiles? Example of missile flight sections in the picture.
Pretty much all missiles ignite a solid-rocket motor called a booster rocket shortly after launch/deployment/firing. Typically, the missile will reach its highest velocity and energy state, shortly after burnout of this booster. After this point, it will lose velocity because of air-drag, or because it lofts its trajectory for various reasons.
Having said that, there are a lot of exceptions. For example, most cruise missiles have some sort of air-breathing motor (e.g. the Tomahawk has a turbofan motor), which will propel the missile. In that case, the booster rocket is only intended to bring the cruise missile up to sustained flying speed, such that the motor can ignite. An interesting application is that of Ramjets: These engines need a certain speed (e.g. Mach 3) to ignite. After ignition of the motor the missile will accelerate even further. A good example is the X-51 waverider experiment in which a Scramjet (a supersonic Ramjet) was tested.
Other missiles feature a sustainer rocket engine, in principle a second rocket motor which burns slower but longer, and keeps the speed of the missile up. Especially air-to-air missiles loft their trajectory directly after launch in order to fly into thinner atmosphere. When these missiles descend again, the speed can be even higher than shortly after launch.
Missiles also do have minimal speed, however this is a bit harder to define as they loose their ability to maneuver gradually with decreasing airspeed. The question is therefore not the minimum speed but rather the mininum maneuverability you are willing to accept.
First: the numbers on that picture indicate range (in kilometers) and altitude (in meters), not speed.
A missile typically does not actively regulate its speed It's turned on, and when the fuel runs out it coasts. Depending on the power of its engine, range to target, flight path, and atmospheric conditions it may or may not reach its maximum aerodynamic speed during its flight time (most will, as most will boost to that speed very rapidly).
Of course a missile, like any object, will bleed energy (thus (max attainable) speed) when turning or climbing and may gain some when diving.
I've not heard of missiles with speed brakes (the only way to actively influence a missile's speed, especially for a missile with a solid rocket motor rather than a turbojet motor like Harpoon) but they may exist (there are bombs with speed brakes to slow their fall for example).
is it possible to somehow estimate the minimum speed of missiles?
Yes, if one treats them like aircraft. Weight, wing area, and coefficient of lift should yield an estimate for minimum airspeed.
However, in application, missiles are built for speed, rather than efficiency, although, as pointed out by U flow and Jim, high subsonic cruise missiles do exist.
And, of course, we have torpedoes, which essentially are underwater "airships", using bouyancy as a source of lift.
But I doubt the crew of the "Craptonesque" could stand the suspense of waiting for anything slower than high subsonic.